AnswersAPSB 2025 Math Essentials-ALPGraphing Two-Variable Linear Inequalities

Graphing Two-Variable Linear Inequalities Answers

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1
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Which is the graph of the linear inequality x – 2y > –6?

Question illustration
A
Option
B
Option
C
Option
D
Option
6

Which statements are true about the linear inequality y > x – 2? Select three options.The slope of the line is –2.The graph of y > x – 2 is a dashed line.The area below the line is shaded.One solution to the inequality is (0, 0).The graph intercepts the y-axis at (0, –2).

Question illustration
A
The slope of the line is –2.
B
The graph of y > x – 2 is a dashed line.
Option B
C
The area below the line is shaded.
D
One solution to the inequality is (0, 0).
E
The graph intercepts the y-axis at (0, –2).
7

Which is the graph of the linear inequality y ≥ −x − 3?

A
On a coordinate plane, a solid straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the right of the line is shaded.
Option A
B
On a coordinate plane, a solid straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the left of the line is shaded.
Option B
C
On a coordinate plane, a dashed straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the right of the line is shaded.
Option C
D
On a coordinate plane, a dashed straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the left of the line is shaded.
Option D
10

Which is the graph of linear inequality 2y > x – 2?

A
Option
B
Option
C
Option
D
Option
11

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Everything to the right of the line is shaded.

Question illustration
A
y ≥ x – 4
Option A
B
y ≤ x – 4
Option B
C
y ≤ x + 4
Option C
D
y ≥ x + 4
Option D
12

On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.

Question illustration
A
y ≤ x − 1
Option A
B
y ≥ x − 1
Option B
C
y < 3x − 1
D
y > 3x − 1
13

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below and to the right of the line is shaded.

Question illustration
A
y ≤ 2x + 4
B
y ≤ x + 3
Option B
C
y ≥ x + 3
Option C
D
y ≥ 2x + 3
14

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 1) and (1, 0). Everything to the left of the line is shaded.

Question illustration
A
(2, 3)
B
(3, –2)
C
(2, 1)
D
(–1, 3)
15

Which is the graph of linear inequality 2y > x – 2?

A
Option
B
Option
C
Option
D
Option
16

Which is the graph of the linear inequality 2x – 3y < 12?

A
Option
B
Option
C
Option
D
Option
17

Which is the graph of the linear inequality y < 3x + 1?

A
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
Option A
B
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
Option B
C
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
Option C
D
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
Option D
18

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded.

Question illustration
A
y ≤ x + 2
Option A
B
y ≥ x + 2
Option B
C
y ≤ x + 2
Option C
D
y ≥ x + 2
Option D
19

Which is the graph of the linear inequality y ≥ −x − 3?

A
On a coordinate plane, a solid straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the right of the line is shaded.
Option A
B
On a coordinate plane, a solid straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the left of the line is shaded.
Option B
C
On a coordinate plane, a dashed straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the right of the line is shaded.
Option C
D
On a coordinate plane, a dashed straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the left of the line is shaded.
Option D

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